A General Actuator Model Based on Nonlinear Equivalent Networks

To facilitate interaction control, variable-impedance actuators have been developed; however, they are fundamentally nonlinear. A general nonlinear actuator model which could be identified unambiguously from observations with the actuator in situ would be useful. Equivalent circuits seem promising because they separate forward path dynamics from interactive dynamics. Can this linear circuit concept be applied to nonlinear systems? In this paper, equivalent circuits are first generalized to comprise two nonlinear parts joined by a linear connector. Modeling actuators in this way reveals an important insight: a Thévenin-type network does not permit unambiguous identification of the forward path dynamics, whereas a Norton-type network does. That is because the Norton source is a zero of the interaction-port operator, whereas the Thévenin source is not. With that insight, an equivalent circuit is further generalized to a network of two nonlinear parts joined nonlinearly, with the restriction that the source/forward path is a zero of the interaction port operator. A Norton-type network in that nonlinear form is unambiguously identifiable. It appears to provide a versatile representation of nonlinear actuators.